Question: $\lim_{x\to \frac{\pi}{2}}\sin(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $-1$ (Choice B) B $0$ (Choice C) C $1$ (Choice D) D The limit doesn't exist.
Solution: $\sin(x)$ is continuous on all points in its domain, and its domain is all real numbers. Therefore, we can find $\lim_{x\to \frac{\pi}{2}}\sin(x)$ by direct substitution. $\begin{aligned} \sin\left(\dfrac{\pi}{2}\right)&=1 \end{aligned}$ $\lim_{x\to \frac{\pi}{2}}\sin(x)=1$